The probability density function of the normal distribution, first
derived by De Moivre and 200 years later by both Gauss and Laplace
independently [R158], is often called the bell curve because of
its characteristic shape (see the example below).

The normal distributions occurs often in nature. For example, it
describes the commonly occurring distribution of samples influenced
by a large number of tiny, random disturbances, each with its own
unique distribution [R158].

Parameters:

loc : float

Mean (“centre”) of the distribution.

scale : float

Standard deviation (spread or “width”) of the distribution.

size : int or tuple of ints, optional

Output shape. If the given shape is, e.g., (m,n,k), then
m*n*k samples are drawn. Default is None, in which case a
single value is returned.

where \mu is the mean and \sigma the standard deviation.
The square of the standard deviation, \sigma^2, is called the
variance.

The function has its peak at the mean, and its “spread” increases with
the standard deviation (the function reaches 0.607 times its maximum at
x + \sigma and x - \sigma[R158]). This implies that
numpy.random.normal is more likely to return samples lying close to the
mean, rather than those far away.